ON THE ASYMPTOTIC-EXPANSION OF HADAMARD-PRODUCTS

We consider functions f and g which are holomorphic on closed sectors in C where they admit an asymptotic representation at oo in the form o f power series in z(-1). We give a simple geometrical condition under which the Hadamard product f g of f and g possesses again an asympto tic expansion at infinity. It turns out that the asymptotic expansion of f g is essentially the formal Hadamard product of the asymptotic expansions of f and g. Our result yields a slight generalization of a well known theorem of W.B. FORD.